In my opinion it is safer than taxi services. I work in Seattle, Washington as a Uber Partner Driver. The process of becoming an Uber Partner Driver was similar to the process of driving a taxi driver. I was already driving a Taxi before I joined Uber. I found driving for Uber much less stressful. Driving a taxi is a very stressful job as you have to worry about the payments and your security. Taxi drivers are never sure what type of customer is getting into the cab. Sometimes customers run away without paying. Because of these distraction which a taxi driver faces on a trip leaves her / him vulnerable of committing mistakes.
But when I started driving for Uber I felt freedom from the stress. I never had to worry about the payment and customer behavior. Rating of customers help me to be prepared for the type of customers I pick. If I pick up a customer with lower rating I know that either the customer will make me wait longer or be somewhat rude. The other helpful feature is GPS which is available inside the App helps a great deal. The pickup and drop-off of customers is also very easy. If you are worried about the insurance coverage, Uber and Taxi service have the same insurance coverage. So in my opinion Uber service is much safer than the taxi service as the driver feels safer and is not distracted.
Uber customer is also safe as their location cab be checked through the app. Uber partner drivers also have to get a background check. But the customers should be careful and should not sit in the car which has a different number plate than the one provided by the app. I have many customers who never check the number plate.